Geometric Signatures as Important Factors to Control the Photo-Stabilities of the Phosphorescent Pd(II)/Pt(II) Complexes: A Case Study

Operation lifetime, as an important parameter, determines the performance of phosphorescent organic light-emitting diodes (OLEDs). Unveiling the intrinsic degradation mechanism of emission material is crucial for improving the operation’s lifetime. In this article, the photo-stabilities of tetradentate transition metal complexes, the popular phosphorescent materials, are explored by means of density functional theory (DFT) and time-dependent (TD)-DFT, aiming to illustrate the geometric signatures as important factors to control the photo-stabilities. Results indicate that for the tetradentate Ni(II), Pd(II), and Pt(II) complexes, the coordinate bonds of the Pt(II) complex exhibit stronger strength. It seems that the strengths of coordinate bonds are closely related to the atomic number of the metal center in the same group, which could be attributed to the various electron configurations. The effect of intramolecular and intermolecular interactions on ligand dissociation is also explored here. The large intramolecular steric hindrance and strong π-π interaction between the Pd(II) complexes caused by aggregation could effectively raise the energy barriers of the dissociation reaction, leading to an unfeasible reaction pathway. Moreover, the aggregation of Pd(II) complex can change the photo-deactivation mechanism as compared to that of monomeric Pd(II) complex, which is favored for avoiding the TTA (triplet-triplet annihilation) process.


Introduction
Pt(II) and Pd(II) complexes have attracted more and more attention because of their excellent virtues. Essentially, the strong spin-orbital coupling (SOC) effect can facilitate the effective intersystem crossing (ISC) process and mixture of singlet and triplet excited states, causing the forbidden T 1 →S 0 transition to become acceptable. The unique property of excited state transformation can promote the application of Pt(II) and Pd(II) complexes in many hot fields. For instance, Pt(II) and Pd(II) complexes can be regarded as phosphorescent emitters in the field of OLEDs. Over the past decades, substantial progress has been made in the development of high-performance Pt(II) and Pd(II) complexes as a result of extensive research within the academic and industrial communities, which has enabled phosphorescent OLEDs to become a main component in state-of-the-art displays between structural signatures, including coordinated forms, aggregation, and intramolecular interaction, and the photostability of tetradentate Pt(II) and Pd(II) complexes? (2) What is the role of aggregation in the photostabilities of Pt(II) and Pd(II) complexes? (3) Can the molecular aggregation of complexes tune the photo-deactivation mechanism? For the sake of completely answering these questions, some Pt(II) and Pd(II) complexes shown in Scheme 1 are chosen, which can explore the role of "metal-coordinate effect", "aggregation effect", and "steric hindrance effect" in the photo-stability. Therein, Pd-1, Pt-2, and Pt-3 are reported in Li and Kim's studies, respectively [19,20]. This study can provide significant and meaningful information for designing stable Pt(II) and Pd(II) complexes used in the fields of phosphorescent probes, prodrugs, and OLEDs.
Molecules 2023, 28, x FOR PEER REVIEW 3 of 14 counterparts. In addition, some significant and meaningful questions can be provided in the investigations of the stabilities of Pt(II) and Pd(II) complexes: (1) What is the relationship between structural signatures, including coordinated forms, aggregation, and intramolecular interaction, and the photostability of tetradentate Pt(II) and Pd(II) complexes? (2) What is the role of aggregation in the photostabilities of Pt(II) and Pd(II) complexes? (3) Can the molecular aggregation of complexes tune the photo-deactivation mechanism? For the sake of completely answering these questions, some Pt(II) and Pd(II) complexes shown in Scheme 1 are chosen, which can explore the role of "metal-coordinate effect", "aggregation effect", and "steric hindrance effect" in the photo-stability. Therein, Pd-1, Pt-2, and Pt-3 are reported in Li and Kim's studies, respectively [19,20]. This study can provide significant and meaningful information for designing stable Pt(II) and Pd(II) complexes used in the fields of phosphorescent probes, prodrugs, and OLEDs. Scheme 1. Chemical structures of studied Pt(II) and Pd(II) complexes, along with the investigated topics.

Computational Details
In this paper, the geometry optimizations and vibrational frequency calculations of ground states (S0), lowest-lying triplet excited states (T1), cation states (+), anion states (−), and lowest-lying singlet excited states (S1) for all the tetradentate Pt(II) and Pd(II) complexes are presented in the methodology of restricted, unrestricted, and time-dependent DFT (RDFT, UDFT, and TDDFT) with the B3LYP hybrid functional [24], respectively. As shown in the previous calculations of various Pt(II) complexes, the B3LYP hybrid functional can well reproduce the experimental results [25][26][27]. The D3BJ dispersion correction [28] was also taken into account. The mix basis sets, including the LANL2DZ basis set [29] and the 6-311G(d,p) basis set [30,31], were used to describe the heavy atoms Pt/Pd and the light atoms (C, H, O, and N). These calculations can be performed in the Gaussian 16 software [32]. Scheme 1. Chemical structures of studied Pt(II) and Pd(II) complexes, along with the investigated topics.

Computational Details
In this paper, the geometry optimizations and vibrational frequency calculations of ground states (S 0 ), lowest-lying triplet excited states (T 1 ), cation states (+), anion states (−), and lowest-lying singlet excited states (S 1 ) for all the tetradentate Pt(II) and Pd(II) complexes are presented in the methodology of restricted, unrestricted, and time-dependent DFT (RDFT, UDFT, and TDDFT) with the B3LYP hybrid functional [24], respectively. As shown in the previous calculations of various Pt(II) complexes, the B3LYP hybrid functional can well reproduce the experimental results [25][26][27]. The D3BJ dispersion correction [28] was also taken into account. The mix basis sets, including the LANL2DZ basis set [29] and the 6-311G(d,p) basis set [30,31], were used to describe the heavy atoms Pt/Pd and the light atoms (C, H, O, and N). These calculations can be performed in the Gaussian 16 software [32].
In the application of optimized geometry to the T 1 excited state, the spin-orbit coupling matrix elements were evaluated, which was realized by means of linear (single residue) response theories. The calculated protocol is the TDDFT with the B3LYP functional, as implemented in the Dalton program [33]. Moreover, the quadratic response theories in the methodology of TDDFT were used to obtain the radiative rate constants. During these computations, the LANL2DZ_ECP and 6-31G for Ir and light atoms are used to balance computational costs and accuracies. The other parameters, including topological parameters of the electron density and Laplacian bond orders, were calculated using Multiwfn_3.8 software [34]. The pictures of geometry, spin density, and interaction region indicator (IRI) analysis were drawn by combining the VMD [35] and Multiwfn_3.8 software.
The molecular dynamics (MD) simulation was performed using the GROMACS 2018.8 software [36] with periodic boundary conditions. A box containing one Pd-1 molecule and 30 mCBP molecules was built by the Packmol program [37]. The NPT ensemble was selected for a duration of 1 ns to obtain a reasonable density at 298 K and 1 bar pressure, followed by a 100 ns NVT production simulation under the same conditions. The GAFF force field [38] was adopted to describe the molecules. The Nosé-Hoover thermostat was used to control the temperature, and the pressure was controlled by the Parrinello-Rahman in an isotropic manner to reach equilibrium.

The Influence of the "Metal-Coordinate Effect" on the Stability of Tetradentate Complexes
In order to explore the bonding nature between the Ni/Pd/Pt and the ligand, the electron localization function (ELF) was carried out here, and two-dimensional color-filled maps of S 0 states are depicted in Figure 1. The two-dimensional color-filled maps of T 1 , S 1 , +, and − states for Ni-1, Pd-1, and Pt-1 are shown in Figures S1-S12. The two-dimensional color-filled ELF maps can be applied to show the coordination electron density localization. As shown in Figure 1, for all complexes, namely Ni-1, Pd-1, and Pt-1, the ELFs between Ni/Pd/Pt and N atoms are smaller than those between Ni/Pd/Pt and C atoms, indicating that the degree of electron localization between Ni/Pd/Pt-N bonds is smaller than that between Ni/Pd/Pt-C bonds. Moreover, from Ni-1 to Pd-1 and Pt-1, the ELF analysis can suggest that the electron between the Pt, N, and C atoms shows gradually localized features in the S 0 , T 1 , S 1 , +, and − states, respectively. In addition, for the Ni-1 complex, compared with the T 1 and S 1 states, it seems that the ELFs between Ni and ligand are smaller than those in the S 0 , +, and − states. On the basis of ELF analyses, one can speculate that, firstly, the electron-localized feature between N and Ni/Pd/Pt atoms could lead to decreased photo-stability of tetradentate Pt(II) complexes. Secondly, the coordinated bond could possess the tendency that, as the atomic number increases, the strengths should increase in the same group of periodic tables of the elements. Thirdly, for the Ni-1 complex, the smaller electron localization between N and Ni in T 1 and S 1 states as compared to those in S 0 , +, and − states imply that the unstable coordinated bonds may be causing the unsatisfactory photo-stability.
Next, a topological analysis was performed to investigate the properties of the coordinate bond further. The corresponding results were collected in Table S1. The parameters of the geometries are shown in Figure S13. The ρ BCP of the Ni/Pd/Pt-N bonds are smaller than the others in the Ni-1 to Pd-1 and Pt-1, which indicates that the ρ(r) values between Ni/Pd/Pt and N are the smallest. Similarly, the ρ(r) values of all coordinate bonds tend to follow the trend in Ni-1 < Pd-1 < Pt-1 as a whole. In the case of Ni-1, the ρ(r) values of Ni-C and Ni-N bonds are also smaller than those in other states. These computed results are consistent with those of the ELF analyses. Here, all ∇ 2 ρ BCP were larger than 0, therefore indicating electron depletion at the BCP. Furthermore, the E BCP values are almost less than or close to 0, which is sufficient to contribute toward bond stabilization [39,40]. The Laplacian bond orders (LBO) of these coordinate bonds were calculated, and the results are summarized in Table 1. Obviously, the LBO of Ni/Pd/Pt-N bonds are considerably smaller than that of the other Ni/Pd/Pt-C bonds. For Ni-1, during the transition from S 0 to T 1 and S 1 , the Ni-N bonds would further weaken. These results demonstrated that the Ni/Pd/Pt-N bonds are the weakest bonds among all complexes, and the sequence of photostabilities may be as follows: Ni-1 < Pd-1 < Pt-1. Next, a topological analysis was performed to investigate the properties of the coordinate bond further. The corresponding results were collected in Table S1. The parameters of the geometries are shown in Figure S13. The ρBCP of the Ni/Pd/Pt-N bonds are smaller than the others in the Ni-1 to Pd-1 and Pt-1, which indicates that the ρ(r) values between Ni/Pd/Pt and N are the smallest. Similarly, the ρ(r) values of all coordinate bonds tend to follow the trend in Ni-1 < Pd-1 < Pt-1 as a whole. In the case of Ni-1, the ρ(r) values of Ni-C and Ni-N bonds are also smaller than those in other states. These computed results are consistent with those of the ELF analyses. Here, all ∇ 2 ρBCP were larger than 0, therefore indicating electron depletion at the BCP. Furthermore, the EBCP values are almost less than or close to 0, which is sufficient to contribute toward bond stabilization [39,40]. The Laplacian bond orders (LBO) of these coordinate bonds were calculated, and the results are summarized in Table 1. Obviously, the LBO of Ni/Pd/Pt-N bonds are considerably smaller than that of the other Ni/Pd/Pt-C bonds. For Ni-1, during the transition from S0 to T1 and S1, the Ni-N bonds would further weaken. These results demonstrated that the Ni/Pd/Pt-N bonds are the weakest bonds among all complexes, and the sequence of photostabilities may be as follows: Ni-1 < Pd-1 < Pt-1.   Finally, the reaction pathways of the Ni/Pd/Pt-N bond breaking were computed to intuitively illustrate the photo-stabilities of Ni-1, Pd-1, and Pt-1, respectively. The corresponding vibration forms of TS are shown in Figures S14-S16. The calculated reaction steps are pictured in Figure 2. For the Ni-1 complex, the energy barriers are 27.06, 18.96, 16.61, 28.35, and 29.52 kcal/mol in the S 0 , T 1 , S 1 , +, and − states, respectively. Seen from these energy barriers, compared to the S 0 , +, and − states, the Ni-1 complex could exhibit weak photo-stability in the T 1 and S 1 states, which are the predominant states involved in the phosphorescent process. For the Pd-1 complex, the Pd-N bond breaking could need to overcome the energy barriers of 23.88, 22.71, 23.15, 27.80, and 24.11 kcal/mol, indicating that the stability of the Pd-1 complex, in comparison, is stronger than that of the Ni-1 complex. In the investigation of stability for Pt-1, larger energy barriers can be needed as compared to those of Ni-1 and Pd-1, and the corresponding values are 30.56, 31.76, 31.68, 35.06, and 30.56 in various states. Analyses of the energy barriers can indicate that, from a structural viewpoint, the stabilities of transition-metal complexes seem to be closely related to the atomic numbers of metal centers in the same group. Additionally, the calculated energy barriers agree with the conclusions of ELF, topological analysis, and Laplacian bond order.
Finally, the reaction pathways of the Ni/Pd/Pt-N bond breaking were computed to intuitively illustrate the photo-stabilities of Ni-1, Pd-1, and Pt-1, respectively. The corresponding vibration forms of TS are shown in Figures S14-S16. The calculated reaction steps are pictured in Figure 2. For the Ni-1 complex, the energy barriers are 27.06, 18.96, 16.61, 28.35, and 29.52 kcal/mol in the S0, T1, S1, +, and -states, respectively. Seen from these energy barriers, compared to the S0, +, and -states, the Ni-1 complex could exhibit weak photo-stability in the T1 and S1 states, which are the predominant states involved in the phosphorescent process. For the Pd-1 complex, the Pd-N bond breaking could need to overcome the energy barriers of 23.88, 22.71, 23.15, 27.80, and 24.11 kcal/mol, indicating that the stability of the Pd-1 complex, in comparison, is stronger than that of the Ni-1 complex. In the investigation of stability for Pt-1, larger energy barriers can be needed as compared to those of Ni-1 and Pd-1, and the corresponding values are 30.56, 31.76, 31.68, 35.06, and 30.56 in various states. Analyses of the energy barriers can indicate that, from a structural viewpoint, the stabilities of transition-metal complexes seem to be closely related to the atomic numbers of metal centers in the same group. Additionally, the calculated energy barriers agree with the conclusions of ELF, topological analysis, and Laplacian bond order.

The Effect of Steric Hindrance on the Stability of Tetradentate Metal Complexes
Here, the effect of intramolecular steric hindrance on the stability of tetradentate Pt(II) complexes, namely Pt-2 and Pt-3, is explored. In order to explore the bonding nature between the Pt and ligand, the ELF, topological analysis of the electron density, and Laplacian bond orders were first calculated, and the results of S0 states are shown in Figure   Figure 2. The reaction pathways of the Ni/Pd/Pt-N bond breaking for Ni-1, Pd-1, and Pt-1 at different states, respectively.

The Effect of Steric Hindrance on the Stability of Tetradentate Metal Complexes
Here, the effect of intramolecular steric hindrance on the stability of tetradentate Pt(II) complexes, namely Pt-2 and Pt-3, is explored. In order to explore the bonding nature between the Pt and ligand, the ELF, topological analysis of the electron density, and Laplacian bond orders were first calculated, and the results of S 0 states are shown in Figure 3, Figures S17-S24 and Tables S2-S3. The parameters of the geometries are shown in Figure S25. As polled in Figure 3, for Pt-2 and Pt-3, the ELFs between Pt, N, and C atoms are similar in different states, implying that the degree of electron localization between Pt-N and Pt-C atom bonds is comparable. Compared with the Pt-C bonds, a smaller electron localization between Pt and N can be found. The ρ BCP and Laplacian bond orders of the Pt-C and N bonds are also applied to demonstrate the reliability of EFL analysis. On the basis of the results of ELF and topological analysis of the electron density and Laplacian bond orders, it can be indicated that the strength of Pt-N bonds, is weaker than that of Pt-C bonds and the substituent can have a negligible influence on the coordinate bonds.
As shown in the results of ELF, topological analysis of the electron density and Laplacian bond orders revealed the reaction pathways of the Pt-N bond breaking for the Pt-2 and Pt-3 at different states, which are shown in Figure 4. The corresponding vibration forms of TS are shown in Figures S26 and S27. For Pt-2, the steps of Pt-N bond breaking would overcome the energy barriers of 22.77, 17.31, 24.56, and 18.80 kcal/mol S 0 , T 1 , +, and − states, respectively. In comparison to Pt-2, larger energy barriers can be achieved, and the corresponding values are 23.94, 19.17, 25.51, and 23.94 kcal/mol, respectively. Although the relative difference in energy barrier is not large enough, the tendency of energy barrier can illustrate that the Pt-N bond breaking of Pt-3 is more difficult than that of Pt-2. According to the experimental results [19], introducing bulky substituents in the Pt(II) complex can enhance the photochemical stability; hence, the calculated results are consistent with the experimental ones. To unveil the role of 3,5-di-tert-butyl-phenyl, only the isosurface map of the IRI of S 0 states was computed because of the similar geometries in excited states. Figure 5 shows the isosurface map of the IRI of S 0 states for Pt-2 and Pt-3 complexes, and sign(λ2)ρ is mapped on the isosurfaces according to the coloring method. The IRI analysis indicates that for the S 0 state of Pt-2, there is a small interaction. Nevertheless, compared with Pt-2, a large intramolecular steric hindrance appears in the S 0 states of Pt-3, which originates from the 3,5-di-tert-butyl-phenyl group.  Figure 3, for Pt-2 and Pt-3, the ELFs between Pt, N, and C atoms are similar in different states, implying that the degree of electron localization between Pt-N and Pt-C atom bonds is comparable. Compared with the Pt-C bonds, a smaller electron localization between Pt and N can be found. The ρBCP and Laplacian bond orders of the Pt-C and N bonds are also applied to demonstrate the reliability of EFL analysis. On the basis of the results of ELF and topological analysis of the electron density and Laplacian bond orders, it can be indicated that the strength of Pt-N bonds, is weaker than that of Pt-C bonds and the substituent can have a negligible influence on the coordinate bonds. As shown in the results of ELF, topological analysis of the electron density and Laplacian bond orders revealed the reaction pathways of the Pt-N bond breaking for the Pt-2 and Pt-3 at different states, which are shown in Figure 4. The corresponding vibration forms of TS are shown in Figures S26 and S27. For Pt-2, the steps of Pt-N bond breaking would overcome the energy barriers of 22.77, 17.31, 24.56, and 18.80 kcal/mol S0, T1, +, and -states, respectively. In comparison to Pt-2, larger energy barriers can be achieved, and the corresponding values are 23.94, 19.17, 25.51, and 23.94 kcal/mol, respectively. Although the relative difference in energy barrier is not large enough, the tendency of energy barrier can illustrate that the Pt-N bond breaking of Pt-3 is more difficult than that of Pt-2. According to the experimental results [19], introducing bulky substituents in the Pt(II) complex can enhance the photochemical stability; hence, the calculated results are consistent with the experimental ones. To unveil the role of 3,5-di-tert-butyl-phenyl, only the isosurface map of the IRI of S0 states was computed because of the similar geometries in excited states. Figure 5 shows the isosurface map of the IRI of S0 states for Pt-2 and Pt-3 complexes, and sign(λ2)ρ is mapped on the isosurfaces according to the coloring method. The IRI analysis indicates that for the S0 state of Pt-2, there is a small interaction. Nevertheless, compared with Pt-2, a large intramolecular steric hindrance appears in the S0 states of Pt-3, which originates from the 3,5-di-tert-butyl-phenyl group.  As shown in the results of ELF, topological analysis of the electron density and Laplacian bond orders revealed the reaction pathways of the Pt-N bond breaking for the Pt-2 and Pt-3 at different states, which are shown in Figure 4. The corresponding vibration forms of TS are shown in Figures S26 and S27. For Pt-2, the steps of Pt-N bond breaking would overcome the energy barriers of 22.77, 17.31, 24.56, and 18.80 kcal/mol S0, T1, +, and -states, respectively. In comparison to Pt-2, larger energy barriers can be achieved, and the corresponding values are 23.94, 19.17, 25.51, and 23.94 kcal/mol, respectively. Although the relative difference in energy barrier is not large enough, the tendency of energy barrier can illustrate that the Pt-N bond breaking of Pt-3 is more difficult than that of Pt-2. According to the experimental results [19], introducing bulky substituents in the Pt(II) complex can enhance the photochemical stability; hence, the calculated results are consistent with the experimental ones. To unveil the role of 3,5-di-tert-butyl-phenyl, only the isosurface map of the IRI of S0 states was computed because of the similar geometries in excited states. Figure 5 shows the isosurface map of the IRI of S0 states for Pt-2 and Pt-3 complexes, and sign(λ2)ρ is mapped on the isosurfaces according to the coloring method. The IRI analysis indicates that for the S0 state of Pt-2, there is a small interaction. Nevertheless, compared with Pt-2, a large intramolecular steric hindrance appears in the S0 states of Pt-3, which originates from the 3,5-di-tert-butyl-phenyl group.

The Effect of the "Aggregation Effect" on the Stability of Tetradentate Metal Complexes
The ELF, topological analysis of the electron density, and Laplacian bond orders were first calculated to illustrate the bonding nature between the Pd and ligand for the Pd-1D and Pd-1T at S 0 and T 1 states, and the results are shown in Figure S28 and Tables S4 and S5. As polled in Figure S8, for Pt-2 and Pt-3, the ELFs between Pt, N, and C atoms are similar in different states, implying that the degree of electron localization between Pt-N and Pt-C atomic bonds is comparable. Compared with the Pt-C bonds, a smaller electron localization between Pt and N can be found. The ρBCP and Laplacian bond orders of the Pt-C and N bonds are also applied to demonstrate the reliability of EFL analysis. On the basis of the results of ELF and topological analysis of the electron density and Laplacian bond orders, it can be indicated that the strength of Pt-N bonds is weaker than that of Pt-C bonds, and the aggregation can have a negligible influence on the coordinate bonds.

The Effect of the "Aggregation Effect" on the Stability of Tetradentate Metal Complexes
The ELF, topological analysis of the electron density, and Laplacian bond orders were first calculated to illustrate the bonding nature between the Pd and ligand for the Pd-1D and Pd-1T at S0 and T1 states, and the results are shown in Figure S28 and Tables S4 and S5. As polled in Figure S8, for Pt-2 and Pt-3, the ELFs between Pt, N, and C atoms are similar in different states, implying that the degree of electron localization between Pt-N and Pt-C atomic bonds is comparable. Compared with the Pt-C bonds, a smaller electron localization between Pt and N can be found. The ρBCP and Laplacian bond orders of the Pt-C and N bonds are also applied to demonstrate the reliability of EFL analysis. On the basis of the results of ELF and topological analysis of the electron density and Laplacian bond orders, it can be indicated that the strength of Pt-N bonds is weaker than that of Pt-C bonds, and the aggregation can have a negligible influence on the coordinate bonds.
For the sake of exhibiting the "aggregation effect" on the stability of tetradentate metal complexes, the reaction pathways of the Pt-N bond breaking of Pd-1, Pd-1D, and Pd-1T are investigated with the help of a rigidity scan. Therein, the Pd-1 is trapped in the host materials, and the molecular dynamics (MD) simulation was performed using the GROMACS 2018.8 software. The corresponding results of rigidity scans for Pd-1, Pd-1D, and Pd-1T are shown in Figure 6. As plotted in Figure 6, the energy barriers of Pd-1D and Pd-1T in S0 and T1 states are far lager than those of Pd-1, indicating that the "aggregation effect" can cause the excellent stability of tetradentate metal complexes. This result is very much in accordance with the experimental investigation. In addition, the large energy barriers pictured in Figure 6 indicate that Pt-N bond breaking is almost impossible at room temperature. For the sake of exhibiting the "aggregation effect" on the stability of tetradentate metal complexes, the reaction pathways of the Pt-N bond breaking of Pd-1, Pd-1D, and Pd-1T are investigated with the help of a rigidity scan. Therein, the Pd-1 is trapped in the host materials, and the molecular dynamics (MD) simulation was performed using the GROMACS 2018.8 software. The corresponding results of rigidity scans for Pd-1, Pd-1D, and Pd-1T are shown in Figure 6. As plotted in Figure 6, the energy barriers of Pd-1D and Pd-1T in S 0 and T 1 states are far lager than those of Pd-1, indicating that the "aggregation effect" can cause the excellent stability of tetradentate metal complexes. This result is very much in accordance with the experimental investigation. In addition, the large energy barriers pictured in Figure 6 indicate that Pt-N bond breaking is almost impossible at room temperature. The isosurface map of IRI states for Pd-1, Pd-1D, and Pd-1T complexes, based on the MD snapshot and geometric optimization, was also carried out to illustrate the intermolecular interaction. The corresponding results were plotted in Figure 7. As exhibited in Figure 7, for the host-guest system, the intermolecular interaction between Pd-1 and mCBP can be classified as π-π interaction and other weak interactions. Compared with the Pd-1 in the doped condition, the isosurface maps of IRI for Pd-1D and Pd-1T in Figure  7 exhibit that there is strong π-π interaction between the Pd(II) complexes. As shown in the Pd-1T complex, the π-π interaction and the middle Pd(II) complex can construct the "sandwich structure" to form the restricted region. This restricted region can effectively constrain the geometric change of the Pd-1T complex, which leads to a high energy barrier for the Pd-1T. In other words, the ligand is restricted in the special region to form the coordinate bonds with Pd, and the dissociation of complexes could originate from the The isosurface map of IRI states for Pd-1, Pd-1D, and Pd-1T complexes, based on the MD snapshot and geometric optimization, was also carried out to illustrate the intermolecular interaction. The corresponding results were plotted in Figure 7. As exhibited in Figure 7, for the host-guest system, the intermolecular interaction between Pd-1 and mCBP can be classified as π-π interaction and other weak interactions. Compared with the Pd-1 in the doped condition, the isosurface maps of IRI for Pd-1D and Pd-1T in Figure 7 exhibit that there is strong π-π interaction between the Pd(II) complexes. As shown in the Pd-1T complex, the π-π interaction and the middle Pd(II) complex can construct the "sandwich structure" to form the restricted region. This restricted region can effectively constrain the geometric change of the Pd-1T complex, which leads to a high energy barrier for the Pd-1T. In other words, the ligand is restricted in the special region to form the coordinate bonds with Pd, and the dissociation of complexes could originate from the bonds of the ligand, which may need a high energy barrier due to the property of covalent bonds. Figure 7, for the host-guest system, the intermolecular interaction between Pd-1 an mCBP can be classified as π-π interaction and other weak interactions. Compared wit the Pd-1 in the doped condition, the isosurface maps of IRI for Pd-1D and Pd-1T in Figur 7 exhibit that there is strong π-π interaction between the Pd(II) complexes. As shown i the Pd-1T complex, the π-π interaction and the middle Pd(II) complex can construct th "sandwich structure" to form the restricted region. This restricted region can effectivel constrain the geometric change of the Pd-1T complex, which leads to a high energy barrie for the Pd-1T. In other words, the ligand is restricted in the special region to form th coordinate bonds with Pd, and the dissociation of complexes could originate from th bonds of the ligand, which may need a high energy barrier due to the property of covalen bonds.

Investigation of the Influence of Transformation between Singlet and Triplet Excited States on Stability
Apart from the investigations of the influence of intramolecular/intermolecular interactions and intrinsic properties on stability, the transformation between singlet and triplet excitons is also considered to explore the effect factor of stability. The calculations of adiabatic singlet and triplet excited states were carried out with the help of Tamm-Dancoff approximation density functional theory (TDA-DFT) in the protocol of B3LYP with LANL2DZ for Pd and6-311G** for C, H, N, and O. The calculated T 1 energies of Pd-1 and Pd-1D are 2.55 eV and 1.98 eV, respectively. In order to further understand the intersystem crossing processes of Pd-1 and Pd-1D, the exploration of the energy-level alignment of singlet and triplet excited states is very significant since the transformation mechanism from singlet to triplet excited states may depend on the energy-level alignment. Hence, the S 1 and T 2 energy levels of Pd-1 and Pd-1D are further computed. As shown in Figure 8, the calculated S 1 /T 2 energies of Pd-1 and Pd-1D in gas phase are calculated to be 2.81 eV/2.73 eV and 2.08 eV/2.33, respectively. It is interesting to note that the S 1 energy of Pd-1 is higher than the T 2 energy. In comparison, the calculated T 2 energy of Pd-1D is higher than the S 1 energy. For the calculated energy-level alignment of Pd-1, due to the competitive spin conversion process (S 1 → T 2 and S 1 → T 1 ), the intersystem crossing (ISC) may be inefficient. On the contrary, in the case of Pd-1D, because of the endothermic energy-level alignment, the ISC is only from S 1 to T 1 , not from S 1 to T 2 . On the basis of the above-mentioned discussion, the phosphorescent process of Pd 1D could be identified as S1 → T1 → S0. However, in the case of the Pd-1 complex, th corresponding process is S1 → T2 →T1→ S0. In comparison to the Pd-1D complex, th complicated photo-physical process of Pd-1 can cause aggregation of triplet density in th emission layer (EML). The long excited state lifetime of triplet excitons is favored for re sulting in a triplet-triplet quenching process. Triplet-triplet annihilation (TTA) and triple polaron annihilation (TPA) are the main degradation mechanisms. Surely, this conclusio needs to be confirmed via more investigation, and herein, only thinking is put forward i our study.
After exploration of the effect of the metal-N coordinate on the stability, the ligan dissociations of Ni-1, Pd-1, Pt-1, Pt-2, and Pt-3 are also investigated. As shown in Figur  S6, the bond dissociation energy of Pd-1 is smaller than that of Ni-1. Among the Ni-1, Pd 1, and Pt-1, the Pt-1 possesses the largest bond dissociation energies in the S0, T1, S1, +, an -states, indicating that the different coordinate circumstances can induce the differen stabilities. In the case of Pt-2 and Pt-3, the bond dissociation energies in the S0, T1, S1, + and -states are comparable, implying that the substituent can cause a slight effect on th stability. In fact, for Ni-1, Pd-1, Pt-1, Pt-2, and Pt-3, the large bond dissociation energie could largely suppress the ligand dissociation. Hence, the investigation of breakage of th metal-N coordinate may be a reasonable strategy to unveil the stability of the tetradentat transition metal complex.
Finally, the dipole moment is also simulated. As shown in the previous study [41 the orientation of metal complexes is related to the dipole moment, and a molecular-scal simulation of the film formation suggested that dipole-dipole interactions tend to hinde alignment in organic films [42,43]. The dipole moments are computed here for Ni-1, Pd To explore the transformation between singlet and triplet excited states in detail, the intersystem crossing (ISC) rates of Pd-1 (S 1 → T 2 and S 1 → T 1 ) and Pd-1D (S 1 → T 1 ) are calculated, which is plotted in Figure 7. The computed intersystem crossing (ISC) rates of Pd-1 (S 1 → T 2 and S 1 → T 1 ) are 1.00 × 10 10 s −1 and 7.44 × 10 9 s −1 , respectively. The computed results indicate that the intersystem crossing (ISC) from S 1 to T 2 is prior to that of S 1 → T 1 . For the Pd-1D, the calculated intersystem crossing (ISC) from S 1 to T 1 is 5.45 × 10 9 s −1 . The radiative decay rates for Pd-1 (T 2 → S 0 and T 1 → S 0 ) and Pd-1D (T 1 → S 0 ) are also computed, and the corresponding values are 4.84 × 10 2 s −1 , 3.79 × 10 4 s −1 , and 4.38 × 10 4 s −1 , respectively. The computed radiative decay rates indicate that for Pd-1, the phosphorescence originated from the T 1 excited state. In addition, compared with the Pd-1, the Pd-1D possesses a larger radiative decay rate, which is beneficial for facilitating the transition of the triplet exciton to the S 0 state.
On the basis of the above-mentioned discussion, the phosphorescent process of Pd-1D could be identified as S 1 → T 1 → S 0 . However, in the case of the Pd-1 complex, the corresponding process is S 1 → T 2 →T 1 → S 0 . In comparison to the Pd-1D complex, the complicated photo-physical process of Pd-1 can cause aggregation of triplet density in the emission layer (EML). The long excited state lifetime of triplet excitons is favored for resulting in a triplet-triplet quenching process. Triplet-triplet annihilation (TTA) and tripletpolaron annihilation (TPA) are the main degradation mechanisms. Surely, this conclusion needs to be confirmed via more investigation, and herein, only thinking is put forward in our study.
After exploration of the effect of the metal-N coordinate on the stability, the ligand dissociations of Ni-1, Pd-1, Pt-1, Pt-2, and Pt-3 are also investigated. As shown in Figure S6, the bond dissociation energy of Pd-1 is smaller than that of Ni-1. Among the Ni-1, Pd-1, and Pt-1, the Pt-1 possesses the largest bond dissociation energies in the S 0 , T 1 , S 1 , +, and − states, indicating that the different coordinate circumstances can induce the different stabilities. In the case of Pt-2 and Pt-3, the bond dissociation energies in the S 0 , T 1 , S 1 , +, and − states are comparable, implying that the substituent can cause a slight effect on the stability. In fact, for Ni-1, Pd-1, Pt-1, Pt-2, and Pt-3, the large bond dissociation energies could largely suppress the ligand dissociation. Hence, the investigation of breakage of the metal-N coordinate may be a reasonable strategy to unveil the stability of the tetradentate transition metal complex.
Finally, the dipole moment is also simulated. As shown in the previous study [41], the orientation of metal complexes is related to the dipole moment, and a molecular-scale simulation of the film formation suggested that dipole-dipole interactions tend to hinder alignment in organic films [42,43]. The dipole moments are computed here for Ni-1, Pd-1, Pt-1, Pt-2, and Pt-3, and the corresponding results are shown in Figure S29. For Ni-1, Pd-1, and Pt-1, the simulated dipole moment vectors are nearly identical, implying that the various mental centers can result in an ignorable effect. In the case of Pt-2, the dipole moment vector is parallel to the molecule. In comparison, for Pt-3, the dipole moment vector is pulled out of the molecular plane. On the basis of the simulated results, it can be inferred that the substituent added to the ligand can cause a distinct change in the dipole moment vector. In some situations, the dipole-dipole interactions do not play a significant role in the orientation of transition metal complexes [44]. Without doubt, the orientation of metal complexes in amorphous films is very complicated and should be explored using more methods.

Conclusions
In this investigation, a systematic investigation of the degradation mechanisms of tetradentate Pt(II) and Pd(II) complexes has been performed to illustrate the geometric signatures as important factors to control the chemical stabilities. The corresponding conclusions can be put forward as follows: (I). Compared with the tetradentate Ni(II) and Pd(II) complexes, the Pt(II) complex possesses more strong coordinate bonds, which suggests that the strengths of coordinate bonds are closely related to the atomic number of the metal center in the same group. (II). The large intramolecular steric hindrance and strong π-π interaction between the complexes originated from aggregation can efficiently constrain the geometric change, raising the energy barriers of the ligand dissociation reaction. (III). In comparison to the monomeric Pd(II) complex, the aggregation of the Pd(II) complex can result in the essential change of the photo-deactivate mechanism and reduce the lifetime of triplet excitability, which is beneficial for avoiding triplet-triplet annihilation.
According to these conclusions, the effect factors of tetradentate metal complexes have been explored in detail. This study can provide meaningful strategies and information for designing high-stability transition metal complexes as phosphorescent materials.